### Wilcoxon Matched-Pair Signed Ranks Test

```Social Science Research Design and Statistics, 2/e
Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
Wilcoxon Matched-Pair Signed
Ranks Test
PowerPoint Prepared by
Alfred P. Rovai
IBM® SPSS® Screen Prints Courtesy of International Business Machines Corporation,
Presentation © 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
Uses of the Wilcoxon Matched-Pair Signed Ranks Test
• The Wilcoxon matched-pair signed ranks test (also called the
Wilcoxon matched pairs test or the Wilcoxon signed ranks
test) is a nonparametric procedure that compares differences
between data pairs of data from two dependent samples.
• It is similar to the related samples sign test except that this test
factors in the size as well as the sign of the paired differences.
• This procedure involves ranking all nonzero difference scores
disregarding sign, reattaching the sign to the rank, and then
evaluating the mean of the positive and the mean of the
negative ranks. Consequently, the Wilcoxon matched-pair
signed ranks test is more powerful than the related sample sign
test and is the preferred test.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
Open the dataset Computer Anxiety.sav.
File available at http://www.watertreepress.com/stats
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
Legacy Dialogs. Alternatively, one can run the test using the Related
Samples option under the Nonparametric Tests menu.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
In this example, we will test the
following null hypothesis:
Ho: There is no difference in
ranks between computer
anxiety pretest and computer
anxiety posttest among
university students.
Move Computer Anxiety Pretest
and Computer Anxiety Posttest
to the Test Pairs: box. Check
Wilcoxon as the Test Type. Click
Options.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
Check Descriptive to generate
descriptive statistics output.
Click Continue and then OK to
run the test.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
SPSS Output
The contents of the SPSS Log is the first output entry. The
Log reflects the syntax used by SPSS to generate the Npar
Tests output.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
SPSS Output
The above SPSS output displays descriptive statistics.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
SPSS Output
The above SPSS output displays ranks statistics. It shows the mean
of the ranks of the difference scores in which posttest computer
anxiety decreased is 49.20 and the mean of the ranks of the
difference scores in which posttest computer anxiety increased is
23.22.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
SPSS Output
The above SPSS output shows that the test is significant using the
z-approximation since the significance level <= .05 (the assumed à
priori significance level).
Note: report the p-value as p < .001. SPSS truncates values; the
SPSS output does not mean that the p-value is zero.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
Follow the menu as indicated to conduct the Wilcoxon test using the
Related Samples option in the Nonparametric Tests menu.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
Select Customize analysis and then
click the Fields tab.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
Move Computer Anxiety Pretest and
Computer Anxiety Posttest to the
Test Fields: box. Click the Settings
tab.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
Select Wilcoxon matched-pair
signed rank (2 samples) box then
select Test Options in the Select an
item: box.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
Note and accept the default settings
by clicking Run to run the test.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
SPSS Output
The contents of the SPSS Log is the first output entry. The
Log reflects the syntax used by SPSS to generate the
Nonparametric Tests output.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
SPSS Output
Test summary statistics are provided above. Double-click the
table in the SPSS output to display details in the Model
Viewer.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
SPSS Output
Additional test output is provided by the
Model Viewer.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
Wilcoxon Matched-Pair Signed Ranks Test Results Summary
H0: There is no difference between the distribution of sense of classroom community
data and a normal distribution. Test results are significant using the z-approximation, z =
5.49, p < .001, indicating a significant decrease in ranks between computer anxiety
pretest and computer anxiety posttest among university students. Effect size using the rapproximation is .59, suggesting a moderate effect size.
Note: when reporting z one may ignore the negative sign provided the direction of
difference is noted in the results. Effect size is calculated using the following formula: r =
z/√N = 5.49/√86 = 5.49/9.27 = 59.
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
End of Presentation
Copyright 2013 by Alfred P. Rovai, Jason D. Baker, and Michael K. Ponton
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